Kai Hao, 36, was shot dead by Khayre in the foyer of the apartment complex where Khayre took a woman hostage on Monday night.
Three officers were wounded in the shootout which ended the siege, and a second man, in addition to the hostage-taker, died from a gunshot wound, police said.
Australia's Prime Minister yesterday vowed to change state laws so that risky criminals are not released from prison early on parole, following a deadly siege by a paroled gunman that the authorities said was an "act of terrorism".
Australia's Prime Minister Malcolm Turnbull said he would speak with state leaders about changing state laws so that risky criminals were not released early on parole.
Police search the home of Yacqub Khayre at Roxburgh Park, Melbourne, Australia, 06 June 2017.
Heavily armed police swarmed the area when a female hostage, believed to be in her 20s, made a triple-0 call telling officers she was being held hostage and a man had been killed.
Australian Prime Minister Malcolm Turnbull said that the incident with Khayre, who had recently been released on parole, would be treated as an act of terrorism.
Regarding the ISIS claim the gunman was a "soldier" of the group, Ashton was again sceptical.
Ashton earlier told Nine Network television that police were aware of the gunman "in relation to terrorism matters, albeit some years ago".
Victoria Police is treating the attack as a terrorist incident and AAP photos show an evidence bag containing a "hardcover book with Arabic writing" was taken from the apartment.
Mr Ashton said Khayre had been on parole since being released from prison in November and 'there was nothing wrong with his parole until yesterday'.
Three police employees suffered injuries during the incidents but they were not life threatening, police said, without elaborating.
On Monday, Khayre booked an appointment with an escort in an apartment building in Brighton and arrived carrying a shotgun, sparking a two-hour siege.
Melbourne's Seven News are reporting that a staff member received a call from a man, thought to be the shooter, just before gunfire rang out on Bay Street.
The Prime Minister responds to the terror attack in Melbourne. The plot was foiled and the Guardian reports Khayre was convicted and later acquitted of involvement in that plot.
Ashton said IS "always tend to jump up and claim responsibility every time something happens" and it was too early to determine whether they were involved.